Geodesic
Existence of the fixed point in the case of evenly contractive monotonic operator
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 160-161

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The article proves the existence of the fixed point in the case of evenly contractive monotonic operator in the Banach $K$-space. It proved to be right that the iterations converge to the fixed point in the metric of the even convergence. Compactness of the invariant set and the total continuity of the operator are not assumed.
Keywords: positive operator; monotonic concave operator; heterotonic operator. 
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     author = {M. L. Katkov},
     title = {Existence of the fixed point in the case of evenly contractive monotonic operator},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {160--161},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a24/}
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M. L. Katkov. Existence of the fixed point in the case of evenly contractive monotonic operator. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 160-161. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a24/